The only people who think that are a small number of those who like their bias. Most of those who like their bias aren't aware of the bleed through - which is abundant.
Obviously those who don't like their bias feel differently, but most of them probably don't recognize this fictional separation either. And that's surely intentional on the part of Fox.
Sure, as Trad points out, everyone can tell the screaming food fights from the rest. But people still expect they are being told the truth by anchors and other main on-screen figures. So when they present one side and not the other, most viewers think that's the whole story. And when their "sources" are "some people say..." most are not skilled enough to filter out the garbage.
The idea that people don't take what O'Reily or Hannity say seriously because "everybody knows they are just entertainment" is facile. Of course people think they are telling them the truth. Not merely the truth, either - but what's important. So when they talk about the need to be energy independent and dismiss or never discuss climate change, that's feeding a narrative that viewers accept as a factual and relevant reflection of what's important in the world.
And, no, it's not just FOX. But FOX does it the most and does the deception part more seemlessly than then rest.
This is part of why we need to have a national conversation about what counts as "press" in the constitutional sense.
WWJD, I'd only dispute your statements in one area. Persuasion is not only part of politics, it's part of life. I certainly persuasion is a part of Fox & CNN. I would not condemn certain talking heads for making persuasion a part of their shows.